Problem: 12 balls numbered 1 through 12 are placed in a bin.  Joe produces a list of three numbers by performing the following sequence three times:  he chooses a ball, records the number, and places the ball back in the bin.   How many different lists are possible?
Solution: There are 12 options for each ball to be drawn, so there are a total of $12^3 = \boxed{1728}$ possible drawings.